Q.Why a signal transmitted from a TV tower cannot be received beyond a certain distance? Write the expression for the optimum separation between the receiving and the transmitting antenna.
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Start your 14-day free trial to unlock the full solution →The Earth's curvature blocks line-of-sight propagation, limiting the range of TV signals. The optimum separation between transmitting and receiving antennas is , where is the Earth's radius and , are the antenna heights.
The Concept: Why TV Signals Have a Range Limit
TV signals in the VHF and UHF bands (used for terrestrial broadcasting) travel in straight lines — they are line-of-sight (LOS) waves. Unlike lower-frequency radio waves that can bend around obstacles or follow the Earth's curvature (ground waves), these higher-frequency signals pass through the ionosphere without reflecting back and are not significantly diffracted by the Earth's bulge.
The Earth is roughly spherical. So even with a powerful transmitter, the signal cannot reach a receiver that lies below the horizon as seen from the transmitting antenna. The curvature of the Earth creates a radio horizon — beyond it, the signal is physically blocked.
This is why you cannot receive a TV tower's signal beyond a certain distance, no matter how strong the transmitter. The limiting factor is geometry, not power.
A common mistake is to think the range is limited by signal attenuation or power loss. While those affect quality, the fundamental limit for VHF/UHF TV is the Earth's curvature blocking the line of sight.
Deriving the Optimum Separation
We want the maximum distance between a transmitting antenna (height ) and a receiving antenna (height ) such that they still have a direct line of sight, just grazing the Earth's surface.
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Set up the geometry.
Consider the Earth as a perfect sphere of radius . Draw the transmitting antenna of height at point , and the receiving antenna of height at point . The line of sight from to just touches the Earth's surface at a point between them. The centres of the Earth, , , and all lie in the same vertical plane.
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Find the distance from the transmitter to the horizon.
From the transmitter at height , draw a tangent to the Earth's surface. This tangent touches the Earth at the horizon point. The distance from the transmitter to this horizon point is the length of the tangent segment.
Using the right-angled triangle formed by the Earth's centre , the transmitter , and the horizon point :
- By Pythagoras:
Since (antenna heights are tens to hundreds of metres, while is 6400 km), we neglect :
- Similarly, find the distance from the receiver to its horizon. …
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